Right Away, All the Way.
The only exception is Alm and Celica, getting them to 15+ is great, but not necessary.
This is because of how promotions work in Gaiden (and Echoes), Instead of set stat bonuses on promotion, stats that are below class base are raised to the new class bases, while other stats remain untouched.
Plus, Characters will have plenty of levels to grow once in their 2nd or 3rd tier. It's common for units to only be in the early levels of tier 3 at endgame.

For this map in particular, there aren't many enemies, and the go to strat is to move/warp someone with high defence, like Lukas, onto the bridge to choke it. I do believe said bridges, like floor tiles in gaiden, give 20 avoid, but I could be wrong. Then just keep squishy units like silk away from the front or on one of the few trees.
With the improved UI and Speed of the remake, this map may take 4-5 min tops on a first playthrough, and maybe even faster without animations.

Honesty, I don't think maps like this one are a big deal.
Sure, it could and maybe should be better, but when played, this map just has the two armies farther apart for 2 or 3 turns, and then everything continues as normal.
It's not like this map is a 30 min long hell filled with ridiculous enemy density and an annoying map gimmick.

I feel like as far as possible additions go, archsage would be nice, but the largest change that I think should be made is female mage promotion time. Maybe standardize it to 12 like the other 2 tier only classes. The promotion to priestess is good, but it isn't so good that it should wait to 20.

OG Gaiden had a few environmental puzzles, but I can't see them adding too many more.
It looks like IS wants to facilitate exploration with the more nonlinear designs, and allowing players to sneak or run past encounters is a huge improvement.
I could see maybe 1 or 2 new environmental puzzles, maybe in the amiibo dungeons, but nothing on the scale of zelda or other adventure games. They are not exactly designed for that purpose.

Time will tell if the dungeon exploration itself will be great, although I hope it will be.
I'm looking forward more to the interior designs of the dungeons. I want to see what the dragon shrine, forest shrine, and and lost woods would look like.

If IS adds difficulty settings more similar to future instalments (Not the normal, paragon mode choice in og gaiden), maybe they could make the summon amount consistent, as suggested above, but also change that amount per difficulty? (2 on normal, 4 on hard, 6 or 8 on lunatic, est.) I could see that being a cool change to many summoner maps, but I could also see the enemy density becoming ridiculous on higher difficulties.
Regardless, consistent amounts of summoned enemies would go far in making summoners more fair and more fun.